We show that the category of abstract elementary classes (AECs) and concrete functors is closed under constructions of ``limit type," which generalizes the approach of Mariano, Zambrano and Villaveces away from the syntactically oriented framework of institutions. Moreover, we provide a broader view of this closure phenomenon, considering a variety of categories of accessible categories with additional structure, and relaxing the assumption that the morphisms be concrete functors.
Keywords: accessible category, abstract elementary class, PIE limit
2010 MSC: 18C35, 03C48, 03C95
Theory and Applications of Categories, Vol. 30, 2015, No. 48, pp 1647-1658.